Dr. Eduardo Reguera said Padilla, who signed with the Dodgers in August, didn't need surgery after spending time at Managua's Metropolitan Hospital.
Police spokesman Vilma Reyes said Wednesday that Padilla's pistol apparently jammed during a target-shooting session late Tuesday.
Padilla handed the pistol to a shooting instructor, a former police captain, who didn't realize there was a bullet in the chamber and shot himself in his hand, Padilla's legal adviser, Roberto Calderon, told The Associated Press. The bullet also grazed Padilla's leg.
The account contradicts Padilla's agent, Adam Katz, who told The Los Angeles Times that it was a "hunting accident."
"He's fine," Katz said, according to the Times.
Dodgers general manager Ned Colletti said he has told Katz the team is interested in re-signing Padilla, who is expected to file for free agency. He said he did not know enough about the incident to say whether it would affect the Dodgers' decision, according to the Times.
Padilla's baseball future appeared uncertain when he was released outright by the Texas Rangers in August. He went 8-6 with a 4.92 ERA in 18 starts for Texas this season.
But the Dodgers, needing immediate help after starter Hiroki Kuroda was hit in the head with a line drive and missed time, gave Padilla another chance. He responded by going 4-0 with a 3.20 ERA down the stretch for the NL West champion Dodgers and turned in two strong postseason outings.
Padilla pitched seven shutout innings against the St. Louis Cardinals in Game 3 of the NLDS as the Dodgers completed a three-game sweep. He held the Philadelphia Phillies to one run in 7 1/3 innings in Game 2 of the NLCS, but was roughed up for six runs in three innings in Game 5 as the Phillies clinched the pennant.
When the Dodgers were knocked out of the playoffs, Padilla said he wanted to return to Los Angeles next season, according to the report.
"They gave me an opportunity," Padilla said, according to the report. "If they give me another opportunity, sure."
Information from The Associated Press was used in this report.